Sample QuestionsSimultaneous (Linear) Equations (Including Problems) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For solving pair of equation $,$ in this exercise use the method of elimination by equating coefficients$:y = 2x - 6; y = 0$
View full solution →Find the value of m $,$ if $x = 2, y = 1$ is a solution of the equation $2x + 3y = m.$
View full solution →A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Geetapaid $\text{Rs}. 27$ for a book kept for seven days, whileMohitpaid $\text{Rs.}21$ for the book he kept for five days. Find the fixed charges and the charge for each extra day.
View full solution →The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10 \ km,$ the charge paid is $\text{Rs.} 315$ and for a journey of $15 \ km,$ the charge paid is $\text{Rs.} 465.$ What are the fixed charges and the charge per kilometer ? How much does a person have to pay for travelling a distance of $32 \ km$ ?
View full solution →$1250$ persons went to sea a circus$-$show. Each adult paid $\text{Rs.} 75$ and each child paid $\text{Rs.} 25$ for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to $\text{Rs.} 61,250.$
View full solution →The age of a man is twice the sum of the ages of his two children. After $20$ years, his age will be equal to the sum of the ages of his children at that time. Find the present age of the man.
View full solution →The sum of two digit number and the number obtained by interchanging the digits of the number is $121.$ If the digits of the number differ by $3,$ find the number.
View full solution →Mr. and Mrs. Ahuja weight $x \mathrm{~kg}$ and $y \mathrm{~kg}$ respectively. They both take a dieting course, at the end of which Mr. Ahuja loses $5 \mathrm{~kg}$ and weights as much as his wife weighed before the course. Mrs. Ahuja loses $4 \mathrm{~kg}$ and weighs $\frac{7}{8}$ th of what her husband weighed before the course. Form two equations in $x$ and $y$, find their weights before taking the dieting course.
View full solution →Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is $3$ find the number.
View full solution →The sum of a two digit number and the number obtained by reversing the order of the digits is $99.$ Find the number, if the digits differ by $3.$
View full solution →$A$ and $B$ both the have some pencils. If $A$ gives $10$ pencils to $B,$ then $B$ will have twice as many as $A$. And if $B$ gives $10$ pencils to $A$, then they will have the same number of pencils. How many pencils does eachhave ?
View full solution →In an examination, the ratio of passes to failures was $4 :1.$ Had $30$ less appeared and $20$ less passed, the ratio of passes to failures would have been $5 :1.$ Find the number of students who appeared for the examination.
View full solution →A part of monthly expenses of a family is constants and the remainingvarywith the number of members in the family. For a family of $4$ person, the total monthly expenses are $Rs. 10,400$ whereas for a family of $7$ persons, the total monthly expenses are $Rs. 15,800$. Find the constant expenses per month and the monthly expenses of each member of a family.
View full solution →The class $XI$ students of school wanted to give a farewell party to the outgoing students of class $XII$. They decided to purchase two kinds of sweets, one costing $Rs. 250$ per $kg$ and other costing $Rs. 350$ per $kg$. They estimated that $40 \ kg$ of sweets were needed. If the total budget for the sweets was $Rs. 11,800$; find how much sweets of each kind were bought ?
View full solution →$90\%$ acid solution $(90\%$ pure acid and $10\%$ water$)$ and $97\%$ acid solution are mixed to obtain $21$ litres of $95\%$ acid solution. How manylitresof each solution are mixed.
View full solution →The sum of digit of a two digit number is $11$. If the digit at ten's place is increased by $5$ and the digit at unit place is decreased by $5$, the digits of the number are found to be reversed. Find the original number.
View full solution →From Delhi station, if we buy $2$ tickets for station $A$ and $3$ tickets for station $B,$ the total cost is $Rs. 77$. But if we buy $3$ tickets for station $A$ and $5$ tickets for station $B$, the total cost is $Rs. 124$. What are the fares from Delhi to station $A$ and to station $B$ ?
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